The co-ordination number rule and the rule of hardness, powerful tools to rationalize inorganic structures

Abstract

Abstract The co-ordination number rule and the rule of hardness are developed in detail to rationalize inorganic co-ordination structures. We demonstrate how even very complex structures can be understood and sometimes predicted starting from primary co-ordination numbers of cations only. We remind the reader of relations between cation and anion co-ordination numbers and their use for the derivation of connectivity formulas of a Niggli type. We show how the hardness of the ions is responsible for their particular position within a structure. Furthermore, we derive a measure of segregation of the different ions within the structures and also of their electrostatic imbalance in relation to Pauling’s rule of charge sums, and we interpret such structural details in the context of simple numeric relations of co-ordination numbers together with specific “chemical” effects.